Block #424,778

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 10:49:19 AM · Difficulty 10.3634 · 6,367,964 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

1032d4604f4dda6f1f68829e339dd623db805af9b898e719557cf72de5cc0e58

View on Chainz ↗

Height

#424,778

Difficulty

10.363408

Transactions

Size

6.15 KB

Version

Bits

0a5d084a

Nonce

115,566

Timestamp

3/1/2014, 10:49:19 AM

Confirmations

6,367,964

Merkle Root

24daf0043829b0bdef5fafdeb926aae590c2d990f64fdf60a3bdef3953ed447f

Transactions (3)

Coinbasedce80fd5e6f2c6…ab83d54d1c3f75

1 in → 1 out9.3798 XPM110 B

AeKNrjNj…1NEq95Ta

6b8f780b0874ca…e6a468d1380172

4 in → 11 out32.1275 XPM873 B

AReS97kW…MJRxRAs7 AYXvVfjC…pKH3vp2n AUF1So9U…9k1XHL4c AcJzPwtv…eezv9oMd Ab1tC7PF…qEx1Dnim

d2627b9f20c4ca…0b5c0b0923c7e4

35 in → 1 out41.2600 XPM5.10 KB

ANj9vq4n…o7EFvPMv

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.373 × 10⁹³(94-digit number)

73733114945351702740…20921202598459375039

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

7.373 × 10⁹³(94-digit number)

73733114945351702740…20921202598459375039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.373 × 10⁹³(94-digit number)

73733114945351702740…20921202598459375041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.474 × 10⁹⁴(95-digit number)

14746622989070340548…41842405196918750079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.474 × 10⁹⁴(95-digit number)

14746622989070340548…41842405196918750081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.949 × 10⁹⁴(95-digit number)

29493245978140681096…83684810393837500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.949 × 10⁹⁴(95-digit number)

29493245978140681096…83684810393837500161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.898 × 10⁹⁴(95-digit number)

58986491956281362192…67369620787675000319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.898 × 10⁹⁴(95-digit number)

58986491956281362192…67369620787675000321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.179 × 10⁹⁵(96-digit number)

11797298391256272438…34739241575350000639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.179 × 10⁹⁵(96-digit number)

11797298391256272438…34739241575350000641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer